LIC, Life Insurance Corporation is India's biggest insurance firm and it is owned by the indian goverment so there is no doubt or worries about security, your money is secure!
Any amount of premium you pay per month guarantees you a good insurance with LIC.
Sometimes the staff is rude and not understanding enough, sometimes the agents are nagging a bit too much so it feels annoying but in my experience that's the problem with all the insurance firms!
LIC recently launched their IPO as well but it wasn't a hit and it soon will be private so people are scared a bit but the structure of the corporation will always remain good so there's no need to worry!
I would recommend you having an insurance with LIC!